A341540 Expansion of the 2-adic integer sqrt(17) that ends in 11.

1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1

Offset

0

Comments

Over the 2-adic integers there are 2 solutions to x^2 = 17, one ends in 01 and the other ends in 11. This sequence gives the latter one. See A341539 for detailed information.

Links

Jianing Song, Table of n, a(n) for n = 0..1000

Formula

a(0) = 1, a(1) = 0; for n >= 2, a(n) = 0 if A341539(n)^2 - 17 is divisible by 2^(n+2), otherwise 1.

a(n) = 1 - A322217(n) for n >= 1.

For n >= 2, a(n) = (A341539(n+1) - A341539(n))/2^n.

Example

If x = ...00000110011001100001011001101100100010111, then x^2 = 10001_2 = 17.

Prog

(PARI) a(n) = if(n==1, 1, truncate(-sqrt(17+O(2^(n+2))))\2^n)

Crossrefs

Cf. A322217, A341539 (successive approximations of the associated 2-adic square root of 17), A318962, A318963 (expansion of sqrt(-7)).

Sequence in context: A296209 A076141 A011751 * A214507 A093709 A079295

Adjacent sequences: A341537 A341538 A341539 * A341541 A341542 A341543

Keyword

nonn,base

Author

Jianing Song, Feb 13 2021

Status

approved